Quantum theory of a mutual-inductance-coupled circuit including Josephson junctions studied via the entangled state representation

Based on the entangled state representation and Feynman’s idea that “electron pairs are bosons, … , a bound pair acts as a Bose particle”, we present a quantization scheme for a mutual-inductance-coupled L C circuit including Josephson junctions. Then we use the Heisenberg equation of motion to obtain the modified operator Josephson equations, which may be useful for quantum control. The variation of the phase-difference operator of the junction with time is also investigated.